Lattice Boltzmann methodsfor Complex Fluids

The lattice Boltzmann method is a mesoscale method
for simulating complex fluids. This is something
traditional CFD cannot do. We have a parallel and
efficient implementation of the lattice Boltzmann
method.

The study of transport phenomena in porous media is
of great interest in fields ranging from oil recovery
and water purification to industrial processes like
catalysis. A great advantage of using
lattice-Boltzmann (or lattice-gas) techniques in
studying flow in porous media is that complex
geometries can be easily implemented and the flow
problem solved therein, since the evolution of the
particle distribution functions can be described in
terms of local collisions with the obstacles using
simple bounce-back boundary conditions.

Synchrotron based X-ray microtomography (XMT)
imaging techniques provide high resolution,
three-dimensional digitised images of rock samples. By
using the lattice-Boltzmann approach in combination
with these high resolution images of rocks, not only it
is possible to compute macroscopic transport
coefficients, such as the permeability of the medium,
but information on local fields, such as velocity or
fluid densities, can also be obtained at the pore
scale. This provides a detailed insight into
local flow characterisation and can help in the
interpretation of experimental measurements, such as
NMR spectroscopy.

2d slice of Bentheimer sandstone from XMT
imaging (left), its bitmap representation to be
used in lattice Bolzmann simulations (center)
and 3d isosurface of the pore space
(right).

Single and two-phase, miscible and immiscible
flow can be simulated in this rock using the
lattice Boltzmann method, and quantities
such
as the rock permeability or relative
permeabilities curves can be computed using
Darcy's law.

The possibility to run large scale
simulations, due to the high scalability
of the lattice Boltzmann method, and to the
availability of high performance computing
resources accessible via the UK RealityGrid and
the US TeraGrid, allows to study the dependence
of permeability and flow patterns on the size
of the sample.

Moreover it consents to study the flow
field in rock samples large enough to capture
the statistics of pores and throat
distributions of the real rock, thus
providing
data that can be meanigfully compared with
experiments.

Visualization of a 512^3 sample of Bentheimer
sandstone (full sample and 2d slice) at a
resolution of 4.9 microns. The pore space is
represented in red and the rock in blue.

The rock wettability can also be defined,
thus permitting to discriminate between the
fluids. In this fashion drainage (non-wetting
phase displacing a wetting phase) and
imbibition (wetting phase displacing non
wetting-phase) processes can be simulated, and
residual fluid distributions can be studied, as
well as the velocity fields and velocity
distribution. Preferred invasion paths and
break-through time can be individuated and
compared with experiments.

Movie from a lattice Boltzmann
simulation showing oil
(non-wetting phase) displacing water from a 512^3 sample of Bentheimer
sandstone.
The oil (represented in blue)
invades from the right.
The rock matrix and the water are not shown.